Trigo dilemma

Geometry Level 4

\[ \left(\sec^{2}10^{\circ}+\tan 10^{\circ}\right)\left(\sec^{2} 50^{\circ} - \tan 50^{\circ}\right)\left(\sec^{2} 70^{\circ}+\tan 70^{\circ}\right)\]

The value of the expression above can be represented in the form \(\dfrac{a-\sqrt{b}}{b}\) where \(a\) and \(b\) are positive coprime integers. Find the value of \(a+b^2\).

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